Gradient moment nulling used as motion artifact suppression technique (MAST) reduces constant velocity motion distortion in standard spin echo or gradient echo pulse sequences. It is an adjustment to zero at the echo time (TE) of the net moments of the amplitude of the waveform of the magnetic field gradients with time. The zeroth moment is the area under the curve. The first moment is the 'center of gravity' etc.
The aim is to minimize the phase shifts acquired by the transverse magnetization of excited nuclei moving along the gradients (including the effect of refocusing radio frequency pulses), particularly for the reduction of image artifacts due to motion.

Quick Overview
Please note that there are different common names for this artifact.

Flow effects in MRI produce a range of artifacts, e.g. intravascular signal void by time of flight effects; turbulent dephasing and first echo dephasing, caused by flowing blood.
Through movement of the hydrogen nuclei (e.g. blood flow), there is a location change between the time these nuclei experience a radio frequency pulse and the time the emitted signal is received (because the repetition time is asynchronous with the pulsatile flow).
The blood flow occasionally produces intravascular high signal intensities due to flow related enhancement, even echo rephasing and diastolic pseudogating. The pulsatile laminar flow within vessels often produces a complex multilayered band that usually propagates outside the head in the phase encoded direction. Blood flow artifacts should be considered as a special subgroup of motion artifacts.

Artifacts can be reduced by reduction of phase shifts with flow compensation (gradient moment nulling), suppression of the blood signal with saturation pulses parallel to the slices, synchronization of the imaging sequence with the heart cycle (cardiac triggering) or can be flipped 90° by swapping the phase//frequency encoding directions.

See also Flow Related Enhancement and Flow Effects.

Flow compensation is based on the principle of even echo rephasing and a function of specific pulse sequences, wherein the application of strategic gradient pulses can compensate for the objectionable spin phase effects of flow motion. Gradient moment nulling of the first order of flow is another adjustment for the reduction of flow artifacts.
Gradient field changes can be configured in such a way that during an echo the magnetization signal vectors for all pixels have zero phase angle independent of velocities, accelerations etc. of the measured tissue. The simplest velocity-compensated pulse sequence is the symmetrical second echo of a spin echo pulse sequence.
Strategic gradient pulses are integrated in special sequences (e.g. CRISP, Complex Rephasing Integrated with Surface Probes) and for the most sequences flow compensation is an optional parameter.

(FRE) Flow related enhancement could be seen most for blood flow, but also for other liquids with some MR imaging techniques, as an increase in intensity due to the washout of saturated spins. FRE provides positive contrast ("bright blood") of vascular details in time of flight MRA as well as the physiologic characterization of blood flow.
If stationary spins within the scanned region experience only an incomplete T1 relaxation between the repeated radio frequency (RF) excitations, this results in fewer signal of the stationary tissue (compared to inflowing blood with completely relaxed spins). The degree of the flow related enhancement is proportional to the blood flow velocity and the used repetition time. The use of flow compensation (gradient moment nulling) improves the FRE especially in gradient echo sequences.

(GMR) The application of strategic gradient pulses can compensate the objectionable spin phase effects of flow motion. That means the reducing of flow effects, e.g. gradient moment nulling of the first order of flow. The simplest velocity-compensated pulse sequence is the symmetrical second echo of a spin echo pulse sequence.
Gradient field changes can be configured in such a way that during an echo the magnetization signal vectors for all pixels have zero phase angle independent of velocities, accelerations etc. of the measured tissue. E.g. the adjustment to zero at the time TE of the net moments of the amplitude of the waveform of the magnetic field gradients with time. The zeroth moment is the area under the curve, the first moment is the 'center of gravity' etc. The aim is to minimize the phase shifts acquired by the transverse magnetization of excited nuclei moving along the gradients (including the effect of refocusing RF pulses), particularly for the reduction of image artifacts due to motion.
Also called Flow Compensation (FC), Motion Artifact Suppression Technique (MAST), Flow motion compression (STILL), Gradient Rephasing (GR), Shimadzu Motion Artifact Reduction Technique (SMART).